Answer:
4.) Silvia had the greater variation in her race results for the season because she has a higher standard deviation.
Step-by-step explanation:
hope this helps!!! :)
The solution is:A mole of gas occupies 22.4 L A liter is 1000 cubic centimeters because 1 cubic centimeter = 1 mL
One Helium molecule (essentially one helium atom) has atomic mass 4 g/mol So for every 22400 cubic centimeters of volume, we have 4 grams of helium Density of helium = 4g / 22400 cm^3 = 1g / 5600 cm^3
Volume of a sphere = (4/3)(pi)r^3 Volume of the outside sphere (the entire sphere) is (4/3)(pi)(R+T)^3 Volume of the inside sphere (the hollow region) is (4/3)(pi)R^3
The difference for the volume of silver. (4/3)(pi)(R+T)^3 - (4/3)(pi)R^3 = (4/3)(pi)(3R^2T + 3RT^2 + T^3)
The density of silver is 10.5g/cm^3
So the mass of the silver is computed by:10.5*(4/3)(pi)(3R^2T + 3RT^2 + T^3) = (14*pi)(3R^2T + 3RT^2 + T^3) = (14pi)T(3R^2 + 3RT + T^2)
Now for the mass of helium: volume x density = (4/3)(pi)R^3 (1/5600) = (pi/4200)R^3
Set the two masses equal: (pi/4200)R^3 = (14pi)T(3R^2 + 3RT + T^2) R^3 = 58800*T(3R^2 + 3RT + T^2) R / T = 58800*(3R^2 + 3RT + T^2) / R^2 = 58800*( 3+T/R^2+(T/R)^2)
then solve for xx = T / R 1/x = 58800*( 3+x/R+x^2) 1/58800 = x (3 + x/R + x^2) 1/58800 = 3x + x^3 x^3 + 3x - 1/58800= 0 x = ~ 5.66893x10^(-6)
Given
we have
Squaring both sides, we have
And finally
Note that, when we square both sides, we have to assume that
because we're assuming that this fraction equals a square root, which is positive.
So, if that fraction is positive you'll actually have roots: choose
and you'll have
Which is a valid solution. If, instead, the fraction is negative, you'll have extraneous roots: choose
and you'll have
Squaring both sides (and here's the mistake!!) you'd have
which is not a solution for the equation, if we plug it in we have
Which is clearly false
Answer:
16 men would be needed to paint the room in 2 hours
Step-by-step explanation:
We can use proportion to solve the problem given, but first we need to determine whether it is a direct or indirect proportion.
If the number of men are increase, the time taken to do the work will decrease, If the number of men are decrease, the time taken to do the work will increase. Therefore, this is an indirect proportion.
We are going to arrange the data inversely.
Let x be the number of men needed to paint the room in two hours
8 hours = 2 hours
x = 4 men
Cross-multiply
2×x = 8×4
2x = 32
Divide both-side of the equation by 2
2x/2 = 32/2
x = 16 men
16 men would be needed to paint the room in 2 hours
